An exothermic reaction is a reaction in which energy is given off, or, in other words, a reaction that has a DeltaH<0 (see: enthalpy).
Here's a potential energy diagram for an exothermic reaction, the combustion of glucose

Notice that the potential energy of the reactants (C_6H_12O_6 + 6O_2) is smaller than the potential energy of the products (6CO_2 + 6H_2O); this difference in potential energy (on this diagram labeled as the energy released by the forward raection or required for the reverse reaction ) represents DeltaH.
We know that DeltaH = H_(f) - H_i, where
H_f represents the enthalpy (potential energy) of the products;
H_i represents the enthalpy (potential energy) of the reactans;
Since H_f is smaller than H_i. DeltaH will be smaller than zero (negative), a value that characterizes exothermic reactions.
So, let's say you would have to draw the diagram for the combustion of glucose. You'd start with the balanced chemical equation
C_6H_12O_6 + 6O_2 -> 6CO_2 + 6H_2O
Then you'd calculate H_i as the sum of the standard state enthalpies (DeltaH_f^@ - usually given to you) of the reactans - each multiplied by their stoichiometric coefficients, and H_f as the sum of the standard state enthalpies of the products - again, each multiplied by their stoichiometric coefficients.
After this point, you'd just graph these values, along with DeltaH = H_(f) - H_(i) <0 (in this case).